2021 SP2: New orthotropic two-way slabs

Tekla Structural Designer
2021
Tekla Structural Designer

2021 SP2: New orthotropic two-way slabs

[TSD-7721] - This new feature enables different stiffnesses to be set for the two orthogonal (X and Y) directions of slabs thus making them orthotropic rather than isotropic (same stiffness in both directions). This can be used to model slab elements that exhibit orthotropic material properties and are assumed to behave in a predominantly “one-way spanning” manner, such as; precast slab units, profiled steel decking, timber decks on floor joists and cross-laminated timber (CLT) elements. For isotropic slabs, the new settings also enable overriding of the global stiffness modification factor for individual slabs. For more comprehensive details see the new Help Topic Orthotropic slabs (and slab specific stiffness adjustments). The picture directly below shows a simple example of results for an orthotropic slab compared to isotropic. Also see the new verification example 1st order linear - Simply supported orthotropic square slab which confirms excellent agreement with theory.
  • Orthotropic behavior is controlled by a new “Analysis Parameters” slab properties group as shown in the picture below. This is available for the Two-way decomposition method for all slab types that have this option. Note the following:

    • These settings apply to the slab entity (e.g. Slab “S 3” in the picture below), not to individual slab items.

    • There is no change to the analytical behavior of One-way decomposition slabs; these are not analyzed and decompose loads in the same idealized, simply-supported one-way manner.
  • While the analytical process and theory involved is complex, we have striven to make using orthotropic slabs as simple and straightforward as possible - the basic process is as follows:

    • To set orthotropic behavior for a slab, simply select any item of the slab then in the Properties Window expand the “Analysis Parameters” group and enable the “Orthotropic” option.

    • Next, with the “Calculate properties” option enabled (the default and recommended option) enter the desired relative stiffness factors for each slab direction; X factor and Y factor (max = 10.0, min = 1.0x10-5).

      • E.g. for the slab to be 10x stiffer in the X direction than the Y direction, enter X factor = 1.0 and Y factor = 0.1.

    • The adjusted slab material stiffness properties to be used in the analysis are then automatically calculated and displayed. These are; Young’s Modulus for each direction Ex and Ey; the Shear moduli In-plane Gxy and out of plane Gxz/Gyz; the Poisson’s ratio for each direction 𝜈x and 𝜈y.

      • Note that the ‘base’ properties from which these derive are the Young’s modulus E and Poisson’s ratio 𝜈 defined in the Materials Database for the slab’s material grade. For more information about the orthotropic material properties and how they are calculated and related see the new Help Topic Orthotropic slab implementation

    • An additional important setting “Apply modification factors” is highlighted in the picture above and is enabled by default. When enabled, the Model Analysis modification factors set via Analyze > Options > Modification Factors are also applied (for more on these see Use of modification factors). Leave this option enabled to model orthotropic behavior together with the usual overall stiffness reduction of the Model modification factors.

      • Note that this setting can also be used to directly control the modification factors for certain slabs which you wish to be different to the model setting while still retaining their isotropic behavior. To do this simply 1) set the X and Y factors to the same value of the specific modification factor you wish to use - e.g. 0.3 - then 2) disable the “Apply modification factors” setting. For more on this see the Help Topic Override global stiffness modification factor with a slab specific factor.

  • Once you have made the desired orthotropic settings as described above, the further process is entirely automatic; simply run analysis and review results to see the effect. The pictures below show an example of this, comparing the results for an isotropic slab supported by beams on the two longer sides only (thus essentially one-way spanning) with a similar slab supported by beam on all four sides; one Isotropic and the other Orthotropic with the settings shown. Note that the slab X-direction is in the shorter span direction.

    • As shown, to achieve highly orthotropic behavior - approaching that of one-way - you can enter a very small factor of e.g. 0.001 in one direction (Y direction in this case), while maintaining the factor of 1.0 for the other direction i.e. making one direction 1000x relatively stiffer than the other.

    • Note that, as for all 2D element results, there can be some sensitivity of results to the mesh size/ shape. Thus a process of convergence testing is advisable - the default slab mesh properties for the mesh size, uniformity factor and mesh type should be reviewed and may need adjusting. As a starting point, it is recommended that the mesh size is no greater than 10% of the shortest edge of the slab item.

      • Note also that one should not expect to achieve perfect, idealized one-way spanning with zero load transfer/ slab forces in the weaker direction - there will always be some small amount of two-way spanning behavior as the example below illustrates.
  • Examining the decomposed beam loads and resulting shears from the FE Load Decomposition , we see that those for the orthotropic case closely approach those for the “one-way” case at the right as shown directly below.

    • For the two-way isotropic case, there is clearly considerable load transfer to the short side beams. The maximum shear on the long-side beams is 25% lower than the one-way spanning case.

    • Conversely, for the orthotropic slab, the maximum shear produced on the long span beams is just 4.5% lower than the one-way spanning case.

    • The picture at the start of this topic shows the slab design moments - both Mdx contours and for a slab strip in the X-direction - for this same example - these again are comparable for the one-way and orthotropic cases.
  • Using the “Calculate Properties” option as described above is the simplest, most robust and thus recommended method of setting orthotropic properties. However, if you know the specific material properties you want to use, you can disable the “Calculate Properties” option and enter them directly, as shown in the picture below. For more information about this method, see the “Define material properties manually” section of the new Help Topic Define orthotropic slab properties. Note the following:

    • The initial properties will take default values based on their state prior to disabling “Calculate Properties” and can then be directly edited.

    • All material properties are editable with the exception of the Poisson’s ratio in the Y direction 𝜈y , since this is defined by the Young’s moduli Ex and Ey and the Poisson’s ratio in the X direction 𝜈x and cannot be independent of these.

      • If you want direct control of 𝜈 for a particular case and direction, you can edit the slab rotation such that the slab X direction is in this direction.
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